An illumination system for EUV projection lithography is known from U.S. Pat. No. 5,361,292, DE 103 17 667 A1, U.S. Pat. No. 2010/0231882 A1 and from U.S. Pat. No. 6,507,440 B1. A facet mirror arranged such that the position of respective facets, the partial beams of which are transferred into the object field in a manner being superimposed, on the facet mirror, that is to say the spatial position of the facets on the facet mirror, predefines an illumination direction, wherein an edge contour of an impingement of the facet mirror simultaneously predefines a field shape of the object field, is known as a so-called specular reflector for example from DE 103 17 667 A1 and U.S. Pat No. 2010/0231882 A1. Hereinafter, such a facet mirror is also referred to as a specular facet mirror and an individual facet of such a facet mirror is also referred to as a specular facet. In the case of the specular reflector according to DE 103 17 667 A1 and according to U.S. Pat No. 2010/0231882 A1, each of the individual facets is again constructed from a multiplicity of individual micromirrors.